Regularization, sparse recovery, and median-of-means tournaments

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• dc.contributor.author Lugosi, Gábor
• dc.contributor.author Mendelson, Shahar
• dc.date.accessioned 2025-12-02T14:22:31Z
• dc.date.available 2025-12-02T14:22:31Z
• dc.date.issued 2019
• dc.date.updated 2025-12-02T14:22:31Z
• dc.description.abstract We introduce a regularized risk minimization procedure for regression function estimation. The procedure is based on median-of-means tournaments, introduced by the authors in Lugosi and Mendelson (2018) and achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. It outperforms standard regularized empirical risk minimization procedures such as LASSO or SLOPE in heavy-tailed problems.
• dc.description.sponsorship Gábor Lugosi was supported by the Spanish Ministry of Economy and Competitiveness, Grant MTM2015-67304-P and FEDER, EU; "High-dimensional problems in structured probabilistic models" -- Ayudas Fundacion BBVA a Equipos de Investigación Científica 2017; and Google Focused Award "Algorithms and Learning for AI". Shahar Mendelson was supported in part by the Israel Science Foundation.
• dc.format.mimetype application/pdf
• dc.identifier.citation Lugosi G, Mendelson S. Regularization, sparse recovery, and median-of-means tournaments. Bernoulli (Andover). 2019;25(3):2075-106. DOI: 10.3150/18-BEJ1046
• dc.identifier.doi http://dx.doi.org/10.3150/18-BEJ1046
• dc.identifier.issn 1350-7265
• dc.identifier.uri http://hdl.handle.net/10230/72104
• dc.language.iso eng
• dc.publisher Bernoulli Society for Mathematical Statistics and Probability
• dc.relation.ispartof Bernoulli: Official Publication of the Bernoulli Society for Mathematical Statistics and Probability. 2019;25(3):2075-2106
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P
• dc.rights © 2019 Bernoulli Society for Mathematical Statistics and Probability
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Lasso
• dc.subject.keyword Median-of-means tournament
• dc.subject.keyword Regularized risk minimization
• dc.subject.keyword Robust regression
• dc.subject.keyword Slope
• dc.title Regularization, sparse recovery, and median-of-means tournaments
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion